Multidimensional Independent Component Analysis Research Articles

Perturbation analysis for matrix joint block diagonalization

The matrix joint block-diagonalization problem (jbdp) of a given matrix set A={Ai}i=1m is about finding a nonsingular matrix W such that all WTAiW are block-diagonal. It includes the matrix joint diagonalization problem (jdp) as a special case for which all WTAiW are required diagonal. Generically, such a matrix W may not exist, but there are practical applications such as multidimensional independent component analysis (MICA) for which it does exist under the ideal situation, i.e., no noise is presented. However, in practice noises do get in and, as a consequence, the matrix set is only approximately block-diagonalizable, i.e., one can only make all W˜TAiW˜ nearly block-diagonal at best, where W˜ is an approximation to W, obtained usually by computation. The main goal of this paper is to develop a perturbation theory for jbdp to address, among others, the question: how accurate this W˜ is. Previously such a theory for jdp has been discussed, but no effort had been attempted for jbdp because, in large part, there is no quantitative way to describe solution uniqueness of jbdp until 2017 when Cai and Liu (2017) [9] successfully obtained a necessary and sufficient uniqueness condition. Based on the condition, in this article, we will establish a perturbation theory for jbdp. Our main contributions include an error bound for the approximate block-diagonalizer W˜ and a backward error analysis for jbdp. Numerical tests are presented to validate the theoretical results.

Multidimensional Blind Separation Using Higher-Order Statistics: Application to Non-Cooperative STBC Systems

Blindly separating the intercepted signals is a challenging problem in non-cooperative multiple input multiple output systems in association with space—time block code (STBC) where channel state information and coding matrix are unavailable. To our knowledge, there is no report on dealing with this problem in literature. In this paper, the STBC systems are represented with an independent component analysis (ICA) model by merging the channel and coding matrices as virtual channel matrix. Analysis shows that the source signals are of group-wise independence and the condition of mutual independence can not be satisfied for ordinary ICA algorithms when specific modulations are employed. A new multidimensional ICA algorithm is proposed to separate the intercepted signals in this case by jointly block-diagonalizing (JBD) the cumulant matrices. In this paper, JBD is achieved by a 2-step optimization algorithm and a contrast function is derived from the JBD criterion to remove the additional permutation ambiguity with explicit mathematical explanations. The convergence of the new method is guaranteed. Compared with the ICA-based channel estimation methods, simulations show that the new algorithm, which does not introduce additional ambiguities, achieves better performance with faster convergence in a non-cooperative scenario.

Multi-dimensional blind separation method for STBC systems

Intercepted signal blind separation is a research topic with high importance for both military and civilian communication systems.A blind separation method for space-time block code (STBC)systems is proposed by using the ordinary independent component analysis (ICA).This method cannot work when specific complex modulations are employed since the assumption of mutual independence cannot be satisfied.The analysis shows that source signals,which are group-wise independent and use multi-dimensional ICA (MICA) instead of ordinary ICA,can be applied in this case.Utilizing the block-diagonal structure of the cumulant matrices,the JADE algorithm is generalized to the multidimensional case to separate the received data into mutually independent groups.Compared with ordinary ICA algorithms,the proposed method does not introduce additional ambiguities.Simulations show that the proposed method overcomes the drawback and achieves a better performance without utilizing coding information than channel estimation based algorithms.

A blind modulation identification algorithm for STBC systems using multidimensional ICA

SUMMARYBlind parameter identification is a research topic of high importance for both military and civilian communication systems. To our knowledge, there is no report in literature on blindly recognizing the modulation of noncooperative MIMO systems in association with space–time block code where channel state information and coding matrix are unavailable. In this paper, we first present a classifier based on maximum likelihood on the condition of virtual channel matrix; second, the modulations are classified into two classes according to the independence of the source signals: independent and groupwise independent constellations. In the next step, a multidimensional independent component analysis algorithm is proposed by utilizing the block‐diagonal structure of the cumulant matrices to estimate the virtual channel matrix for these two cases, respectively. Last, the ambiguities are removed partly, and the classifier is proven to be insensitive to the remaining indeterminacy. Parallel computation technique is adopted to accelerate the computation of the logarithm likelihood function. Simulations show that our algorithm can work with high recognition probabilities in noncooperative space–time block code communication systems. Copyright © 2013 John Wiley & Sons, Ltd.

Numerical simulation and analysis based on multidimensional independent component analysis

By introducing an indicator to evaluate performance of Multidimensional Independent Component Analysis(MICA) algorithm,the separation was studied by numerical simulation.The multidimensional Amari separation error was used as an important indicator of the measurement of MICA algorithm performance.In the comparative separation performance analysis of four algorithms named vkMICA,cfMICA,MSOBI,SJADE,a random distribution of letters signal was used for simulation and testing,and a visual representation of MICA model of separation and uncertainty was got.The results show that MICA is a very effective method for multidimensional source signal analysis.

Automatic Identification of Functional Clusters in fMRI Data Using Spatial Dependence

In independent component analysis (ICA) of functional magnetic resonance imaging (fMRI) data, extracting a large number of maximally independent components provides a detailed functional segmentation of brain. However, such high-order segmentation does not establish the relationships among different brain networks, and also studying and classifying components can be challenging. In this study, we present a multidimensional ICA (MICA) scheme to achieve automatic component clustering. In our MICA framework, stable components are hierarchically grouped into clusters based on higher order statistical dependence--mutual information--among spatial components, instead of the typically used temporal correlation among time courses. The final cluster membership is determined using a statistical hypothesis testing method. Since ICA decomposition takes into account the modulation of the spatial maps, i.e., temporal information, our ICA-based approach incorporates both spatial and temporal information effectively. Our experimental results from both simulated and real fMRI datasets show that the use of spatial dependence leads to physiologically meaningful connectivity structure of brain networks, which is consistently identified across various ICA model orders and algorithms. In addition, we observe that components related to artifacts, including cerebrospinal fluid, arteries, and large draining veins, are grouped together and encouragingly distinguished from other components of interest.

Dependent Component Analysis: Concepts and Main Algorithms

Dependent Component Analysis(DCA) as an extension of Independent Component Analysis(ICA) for Blind Source Separation(BSS) has more applications than ICA and received more and more attentions during the last several years in the study of signal processing and neural networks. After a general and detailed definition of the DCA model is given, the separateness and uniqueness of the DCA model ha ve been discussed in theory . Then , the state-of-art DC A algorithms are overviewed, these methods include multidimensional ICA, v ariance dependent BSS, s ubband d ecomposition ICA , maximum non-Gaussianity method, Wold decomposition method and time-frequency method are constructed for the BSS problem in theories and some simulations of the se algorithms are also exhibited for different applications .

MULTIDIMENSIONAL INDEPENDENT COMPONENT ANALYSIS FOR STATISTICAL ESTIMATIONS OF INDETERMINACIES IN ELECTROCARDIOGRAMS

Independent component analysis (ICA) is a technique capable of separating independent components (ICs) from complex electrocardiogram (ECG) signals. The basic intention behind using multidimensional independent component analysis (MICA) is to find stable higher dimensional source signal subspaces. This study highlights the ability of ICA for parametrization of ECG signals to reduce the amount of redundant ECG data if any in a data set. The aim of this paper is to justify the underlying theory of the use of ICA and how it can be extended to for MICA separation of the ECG signals for combinational leads to attain most useful diagnostic information, which was not discussed in other some similar previous publications in this field. It is also investigated that the value of kurtosis coefficients for the ICs, which represents the noise component, can be further reduced using parametrized multidimensional independent component analysis (PMICA) technique. The indeterminacies available in the ECG data are also analyzed using modified version of Jade algorithm for PMICA and parametrized standard independent component analysis (PSICA). For the ECG data set, Jade algorithm is applied first to find smaller subspaces for MICA analysis and can therefore be regarded as a basis algorithm for PMICA analysis. The simulation results are obtained in Matlab environment to indicate that, ICA can definitely improve signal–noise ratio (SNR) in minimizing the reconstruction errors. The future scope of MICA expected by author is that, by reconsidering the notion of ICA, a more general perspective can be envisioned: i.e. modified multidimensional independent component analysis (MMICA). It would be based on a morphological geometric parametrization (MGP) which would further reduce the indeterminacies involved in matrix-based modeling (MBM).

Time-Domain Blind Signal Separation of Convolutive Mixtures via Multidimensional Independent Component Analysis

An algorithm for blind signal separation (BSS) of convolutive mixtures is presented. In this algorithm, the BSS problem is treated as multidimensional independent component analysis (ICA) by introducing an extended signal vector which is composed of current and previous samples of signals. It is empirically known that a number of conventional ICA algorithms solve the multidimensional ICA problem up to permutation and scaling of signals. In this paper, we give theoretical justification for using any conventional ICA algorithm. Then, we discuss the remaining problems, i.e., permutation and scaling of signals. To solve the permutation problem, we propose a simple algorithm which classifies the signals obtained by a conventional ICA algorithm into mutually independent subsets by utilizing temporal structure of the signals. For the scaling problem, we prove that the method proposed by Koldovský and Tichavský is theoretically proper in respect of estimating filtered versions of source signals which are observed at sensors.

Detection of Indeterminacies in Corrected ECG Signals Using Parameterized Multidimensional Independent Component Analysis

Independent component analysis (ICA) is a new technique suitable for separating independent components from electrocardiogram (ECG) complex signals. The basic idea of using multidimensional independent component analysis (MICA) is to find stable higher dimensional source signal subspaces and to decompose each rotation into elementary rotations within all two‐dimensional planes spanned by the coordinate axes useful for diagnostic information of heart. In this paper, ability of ICA for parameterization of ECG signals was felt to reduce the amount of redundant ECG data. This work aims at finding an independent subspace analysis (ISA) model for ECG analysis that allows applicability to any random vectors available in an ECG data set. For the common standards for electrocardiography (CSE) based ECG data sets, joint approximate diagonalization of eigen matrices (Jade) algorithm is used to find smaller subspaces. The extracted independent components are further cleaned by statistical measures. In this study, it is also observed that the value of kurtosis coefficients for the independent components, which represents the noise component, can be further reduced using parameterized multidimensional ICA (PMICA) technique. The indeterminacies if available in the ECG data are to be analysed also using modified version of Jade algorithm to PMICA and parameterized standard ICA (PsICA) for comparative studies. The indeterminacies if available in the ECG data are reduced in PMICA better in comparison to the analysis done using PsICA. The simulation results obtained indicate that ICA definitely improves signal–noise ratio (SNR) like the other higher order digital filtering methods like Kalman, Butterworth etc. with minimum reconstruction errors. Here, it is also confirmed that re‐parameterization of the standard ICA model results into a ‘component model’ using MICA technique, which is geometric in spirit and free of indeterminacies existing in sICA model.

Style subspaces for character animation

AbstractIn this paper, we present a novel method for editing stylistic human motions. We represent styles as differences between stylistic and introduced neutral motions, including timing differences and spatial differences. Timing differences are defined as time alignment curves, while spatial differences are found by a machine learning technique: independent feature subspaces analysis, which is the combination of multidimensional independent component analysis and invariant feature subspaces. This technique is used to decompose two motions into several subspaces. One of these subspaces can be defined as style subspace that describes the style aspects of the stylistic motion. In order to find the style subspace, we compare norms of the projections of two motions on each subspace. Once the time alignment curves and style subspaces of several motion clips are obtained, animators can tune, transfer, and merge the style subspaces to synthesize new motion clips with various styles. Our method is easy to use since manual manipulations and large training data sets are not necessary. Copyright © 2008 John Wiley & Sons, Ltd.

Uniqueness of complex and multidimensional independent component analysis

A complex version of the Darmois–Skitovitch theorem is proved using a multivariate extension of the latter by Ghurye and Olkin. This makes it possible to calculate the indeterminacies of independent component analysis (ICA) with complex variables and coefficients. Furthermore, the multivariate Darmois–Skitovitch theorem is used to show uniqueness of multidimensional ICA, where only groups of sources are mutually independent.

On the relation between discriminant analysis and mutual information for supervised linear feature extraction

This paper provides a unifying view of three discriminant linear feature extraction methods: linear discriminant analysis, heteroscedastic discriminant analysis and maximization of mutual information. We propose a model-independent reformulation of the criteria related to these three methods that stresses their similarities and elucidates their differences. Based on assumptions for the probability distribution of the classification data, we obtain sufficient conditions under which two or more of the above criteria coincide. It is shown that these conditions also suffice for Bayes optimality of the criteria. Our approach results in an information-theoretic derivation of linear discriminant analysis and heteroscedastic discriminant analysis. Finally, regarding linear discriminant analysis, we discuss its relation to multidimensional independent component analysis and derive suboptimality bounds based on information theory.